We evaluate the zero-point renormalization (ZPR) due to electron-phonon interactions of 28 solids using the projector-augmented-wave (PAW) method. The calculations cover diamond, many zincblende semiconductors, rock-salt and wurtzite oxides, as well as silicate and titania. Particular care is taken to include long-range electrostatic interactions via a generalized Fröhlich model. The data are compared to recent calculations [Miglio et al., npj Comput. Mater. 6, 167 (2020)] and generally very good agreement is found. We discuss in detail the evaluation of the electron-phonon matrix elements within the PAW method. We show that two distinct versions can be obtained depending on when the atomic derivatives are taken. If the PAW transformation is applied before taking derivatives with respect to the ionic positions, then equations similar to the ones conventionally used in pseudopotential codes are obtained. If the PAW transformation is used after taking the derivatives, then the full-potential spirit is largely maintained. We show that both variants yield very similar ZPRs for selected materials when the rigid-ion approximation is employed. In practice, we find, however, that the pseudoversion converges more rapidly with respect to the number of included unoccupied states.

中文翻译：

---

使用投影增强波法对半导体和绝缘体的带隙进行零点重整化

我们使用投影仪增强波 (PAW) 方法评估了由于 28 个固体的电子-声子相互作用导致的零点重整化 (ZPR)。计算涵盖金刚石、许多闪锌矿半导体、岩盐和纤锌矿氧化物，以及硅酸盐和二氧化钛。特别注意通过广义 Fröhlich 模型包括长程静电相互作用。这些数据与最近的计算进行了比较 [Miglio et al. , npj 计算。母校。 6, 167 (2020)] 并且通常发现非常好的一致性。我们详细讨论了 PAW 方法中电子 - 声子矩阵元素的评估。我们表明，取决于何时采用原子导数，可以获得两个不同的版本。如果在对离子位置求导之前应用 PAW 变换，则获得与赝势代码中常规使用的方程相似的方程。如果在取导数后使用 PAW 变换，则很大程度上保持了全势精神。我们表明，当采用刚性离子近似时，两种变体对选定的材料产生非常相似的 ZPR。然而，在实践中，我们发现伪版本相对于包含的未占用状态的数量收敛得更快。